Large language models (LLMs) have shown remarkable in-context learning (ICL) capabilities on textual data. We explore whether these capabilities can be extended to continuous vectors from diverse domains, obtained from black-box pretrained encoders. By aligning input data with an LLM's embedding space through lightweight projectors, we observe that LLMs can effectively process and learn from these projected vectors, which we term Vector-ICL. In particular, we find that pretraining projectors with general language modeling objectives enables Vector-ICL, while task-specific finetuning further enhances performance. In our experiments across various tasks and modalities, including text reconstruction, numerical function regression, text classification, summarization, molecule captioning, time-series classification, graph classification, and fMRI decoding, Vector-ICL often surpasses both few-shot ICL and domain-specific model or tuning. We further conduct analyses and case studies, indicating the potential of LLMs to process vector representations beyond traditional token-based paradigms.
Although modern imaging technologies allow us to study connectivity between two distinct brain regions in-vivo, an in-depth understanding of how anatomical structure supports brain function and how spontaneous functional fluctuations emerge remarkable cognition is still elusive. Meanwhile, tremendous efforts have been made in the realm of machine learning to establish the nonlinear mapping between neuroimaging data and phenotypic traits. However, the absence of neuroscience insight in the current approaches poses significant challenges in understanding cognitive behavior from transient neural activities. To address this challenge, we put the spotlight on the coupling mechanism of structural connectivity (SC) and functional connectivity (FC) by formulating such network neuroscience question into an expressive graph representation learning problem for high-order topology. Specifically, we introduce the concept of topological detour to characterize how a ubiquitous instance of FC (direct link) is supported by neural pathways (detour) physically wired by SC, which forms a cyclic loop interacted by brain structure and function. In the clich\'e of machine learning, the multi-hop detour pathway underlying SC-FC coupling allows us to devise a novel multi-head self-attention mechanism within Transformer to capture multi-modal feature representation from paired graphs of SC and FC. Taken together, we propose a biological-inspired deep model, coined as NeuroPath, to find putative connectomic feature representations from the unprecedented amount of neuroimages, which can be plugged into various downstream applications such as task recognition and disease diagnosis. We have evaluated NeuroPath on large-scale public datasets including HCP and UK Biobank under supervised and zero-shot learning, where the state-of-the-art performance by our NeuroPath indicates great potential in network neuroscience.
With the prosperity of contrastive learning for visual representation learning (VCL), it is also adapted to the graph domain and yields promising performance. However, through a systematic study of various graph contrastive learning (GCL) methods, we observe that some common phenomena among existing GCL methods that are quite different from the original VCL methods, including 1) positive samples are not a must for GCL; 2) negative samples are not necessary for graph classification, neither for node classification when adopting specific normalization modules; 3) data augmentations have much less influence on GCL, as simple domain-agnostic augmentations (e.g., Gaussian noise) can also attain fairly good performance. By uncovering how the implicit inductive bias of GNNs works in contrastive learning, we theoretically provide insights into the above intriguing properties of GCL. Rather than directly porting existing VCL methods to GCL, we advocate for more attention toward the unique architecture of graph learning and consider its implicit influence when designing GCL methods. Code is available at https: //github.com/PKU-ML/ArchitectureMattersGCL.
Graph neural networks have become the default choice by practitioners for graph learning tasks such as graph classification and node classification. Nevertheless, popular graph neural network models still struggle to capture higher-order information, i.e., information that goes \emph{beyond} pairwise interactions. Recent work has shown that persistent homology, a tool from topological data analysis, can enrich graph neural networks with topological information that they otherwise could not capture. Calculating such features is efficient for dimension 0 (connected components) and dimension 1 (cycles). However, when it comes to higher-order structures, it does not scale well, with a complexity of $O(n^d)$, where $n$ is the number of nodes and $d$ is the order of the structures. In this work, we introduce a novel method that extracts information about higher-order structures in the graph while still using the efficient low-dimensional persistent homology algorithm. On standard benchmark datasets, we show that our method can lead to up to $31\%$ improvements in test accuracy.
Graph distillation has emerged as a solution for reducing large graph datasets to smaller, more manageable, and informative ones. Existing methods primarily target node classification, involve computationally intensive processes, and fail to capture the true distribution of the full graph dataset. To address these issues, we introduce Graph Distillation with Structural Attention Matching (GSTAM), a novel method for condensing graph classification datasets. GSTAM leverages the attention maps of GNNs to distill structural information from the original dataset into synthetic graphs. The structural attention-matching mechanism exploits the areas of the input graph that GNNs prioritize for classification, effectively distilling such information into the synthetic graphs and improving overall distillation performance. Comprehensive experiments demonstrate GSTAM's superiority over existing methods, achieving 0.45% to 6.5% better performance in extreme condensation ratios, highlighting its potential use in advancing distillation for graph classification tasks (Code available at https://github.com/arashrasti96/GSTAM).
Data augmentation is widely used for training a neural network given little labeled data. A common practice of augmentation training is applying a composition of multiple transformations sequentially to the data. Existing augmentation methods such as RandAugment randomly sample from a list of pre-selected transformations, while methods such as AutoAugment apply advanced search to optimize over an augmentation set of size $k^d$, which is the number of transformation sequences of length $d$, given a list of $k$ transformations. In this paper, we design efficient algorithms whose running time complexity is much faster than the worst-case complexity of $O(k^d)$, provably. We propose a new algorithm to search for a binary tree-structured composition of $k$ transformations, where each tree node corresponds to one transformation. The binary tree generalizes sequential augmentations, such as the SimCLR augmentation scheme for contrastive learning. Using a top-down, recursive search procedure, our algorithm achieves a runtime complexity of $O(2^d k)$, which is much faster than $O(k^d)$ as $k$ increases above $2$. We apply our algorithm to tackle data distributions with heterogeneous subpopulations by searching for one tree in each subpopulation and then learning a weighted combination, resulting in a forest of trees. We validate our proposed algorithms on numerous graph and image datasets, including a multi-label graph classification dataset we collected. The dataset exhibits significant variations in the sizes of graphs and their average degrees, making it ideal for studying data augmentation. We show that our approach can reduce the computation cost by 43% over existing search methods while improving performance by 4.3%. The tree structures can be used to interpret the relative importance of each transformation, such as identifying the important transformations on small vs. large graphs.
Theoretical studies on the representation power of GNNs have been centered around understanding the equivalence of GNNs, using WL-Tests for detecting graph isomorphism. In this paper, we argue that such equivalence ignores the accompanying optimization issues and does not provide a holistic view of the GNN learning process. We illustrate these gaps between representation and optimization with examples and experiments. We also explore the existence of an implicit inductive bias (e.g. fully connected networks prefer to learn low frequency functions in their input space) in GNNs, in the context of graph classification tasks. We further prove theoretically that the message-passing layers in the graph, have a tendency to search for either discriminative subgraphs, or a collection of discriminative nodes dispersed across the graph, depending on the different global pooling layers used. We empirically verify this bias through experiments over real-world and synthetic datasets. Finally, we show how our work can help in incorporating domain knowledge via attention based architectures, and can evince their capability to discriminate coherent subgraphs.
Persistent homology, a fundamental technique within Topological Data Analysis (TDA), captures structural and shape characteristics of graphs, yet encounters computational difficulties when applied to dynamic directed graphs. This paper introduces the Dynamic Neural Dowker Network (DNDN), a novel framework specifically designed to approximate the results of dynamic Dowker filtration, aiming to capture the high-order topological features of dynamic directed graphs. Our approach creatively uses line graph transformations to produce both source and sink line graphs, highlighting the shared neighbor structures that Dowker complexes focus on. The DNDN incorporates a Source-Sink Line Graph Neural Network (SSLGNN) layer to effectively capture the neighborhood relationships among dynamic edges. Additionally, we introduce an innovative duality edge fusion mechanism, ensuring that the results for both the sink and source line graphs adhere to the duality principle intrinsic to Dowker complexes. Our approach is validated through comprehensive experiments on real-world datasets, demonstrating DNDN's capability not only to effectively approximate dynamic Dowker filtration results but also to perform exceptionally in dynamic graph classification tasks.
Graph Transformers (GTs) have recently achieved significant success in the graph domain by effectively capturing both long-range dependencies and graph inductive biases. However, these methods face two primary challenges: (1) multi-view chaos, which results from coupling multi-view information (positional, structural, attribute), thereby impeding flexible usage and the interpretability of the propagation process. (2) local-global chaos, which arises from coupling local message passing with global attention, leading to issues of overfitting and over-globalizing. To address these challenges, we propose a high-level decoupled perspective of GTs, breaking them down into three components and two interaction levels: positional attention, structural attention, and attribute attention, alongside local and global interaction. Based on this decoupled perspective, we design a decoupled graph triple attention network named DeGTA, which separately computes multi-view attentions and adaptively integrates multi-view local and global information. This approach offers three key advantages: enhanced interpretability, flexible design, and adaptive integration of local and global information. Through extensive experiments, DeGTA achieves state-of-the-art performance across various datasets and tasks, including node classification and graph classification. Comprehensive ablation studies demonstrate that decoupling is essential for improving performance and enhancing interpretability. Our code is available at: https://github.com/wangxiaotang0906/DeGTA
Graph out-of-distribution (OOD) generalization remains a major challenge in graph learning since graph neural networks (GNNs) often suffer from severe performance degradation under distribution shifts. Invariant learning, aiming to extract invariant features across varied distributions, has recently emerged as a promising approach for OOD generation. Despite the great success of invariant learning in OOD problems for Euclidean data (i.e., images), the exploration within graph data remains constrained by the complex nature of graphs. Existing studies, such as data augmentation or causal intervention, either suffer from disruptions to invariance during the graph manipulation process or face reliability issues due to a lack of supervised signals for causal parts. In this work, we propose a novel framework, called Invariant Graph Learning based on Information bottleneck theory (InfoIGL), to extract the invariant features of graphs and enhance models' generalization ability to unseen distributions. Specifically, InfoIGL introduces a redundancy filter to compress task-irrelevant information related to environmental factors. Cooperating with our designed multi-level contrastive learning, we maximize the mutual information among graphs of the same class in the downstream classification tasks, preserving invariant features for prediction to a great extent. An appealing feature of InfoIGL is its strong generalization ability without depending on supervised signal of invariance. Experiments on both synthetic and real-world datasets demonstrate that our method achieves state-of-the-art performance under OOD generalization for graph classification tasks. The source code is available at https://github.com/maowenyu-11/InfoIGL.
In this paper, we introduce AutoRDF2GML, a framework designed to convert RDF data into data representations tailored for graph machine learning tasks. AutoRDF2GML enables, for the first time, the creation of both content-based features -- i.e., features based on RDF datatype properties -- and topology-based features -- i.e., features based on RDF object properties. Characterized by automated feature extraction, AutoRDF2GML makes it possible even for users less familiar with RDF and SPARQL to generate data representations ready for graph machine learning tasks, such as link prediction, node classification, and graph classification. Furthermore, we present four new benchmark datasets for graph machine learning, created from large RDF knowledge graphs using our framework. These datasets serve as valuable resources for evaluating graph machine learning approaches, such as graph neural networks. Overall, our framework effectively bridges the gap between the Graph Machine Learning and Semantic Web communities, paving the way for RDF-based machine learning applications.
Graph classification is a critical task in numerous multimedia applications, where graphs are employed to represent diverse types of multimedia data, including images, videos, and social networks. Nevertheless, in real-world scenarios, labeled graph data can be limited or scarce. To address this issue, we focus on the problem of semi-supervised graph classification, which involves both supervised and unsupervised models learning from labeled and unlabeled data. In contrast to recent approaches that transfer the entire knowledge from the unsupervised model to the supervised one, we argue that an effective transfer should only retain the relevant semantics that align well with the supervised task. In this paper, we propose a novel framework named DisenSemi, which learns disentangled representation for semi-supervised graph classification. Specifically, a disentangled graph encoder is proposed to generate factor-wise graph representations for both supervised and unsupervised models. Then we train two models via supervised objective and mutual information (MI)-based constraints respectively. To ensure the meaningful transfer of knowledge from the unsupervised encoder to the supervised one, we further define an MI-based disentangled consistency regularization between two models and identify the corresponding rationale that aligns well with the current graph classification task. Experimental results on a range of publicly accessible datasets reveal the effectiveness of our DisenSemi.
HyperAggregation is a hypernetwork-based aggregation function for Graph Neural Networks. It uses a hypernetwork to dynamically generate weights in the size of the current neighborhood, which are then used to aggregate this neighborhood. This aggregation with the generated weights is done like an MLP-Mixer channel mixing over variable-sized vertex neighborhoods. We demonstrate HyperAggregation in two models, GraphHyperMixer is a model based on MLP-Mixer while GraphHyperConv is derived from a GCN but with a hypernetwork-based aggregation function. We perform experiments on diverse benchmark datasets for the vertex classification, graph classification, and graph regression tasks. The results show that HyperAggregation can be effectively used for homophilic and heterophilic datasets in both inductive and transductive settings. GraphHyperConv performs better than GraphHyperMixer and is especially strong in the transductive setting. On the heterophilic dataset Roman-Empire it reaches a new state of the art. On the graph-level tasks our models perform in line with similarly sized models. Ablation studies investigate the robustness against various hyperparameter choices. The implementation of HyperAggregation as well code to reproduce all experiments is available under https://github.com/Foisunt/HyperAggregation .
Graph classification benchmarks, vital for assessing and developing graph neural networks (GNNs), have recently been scrutinized, as simple methods like MLPs have demonstrated comparable performance. This leads to an important question: Do these benchmarks effectively distinguish the advancements of GNNs over other methodologies? If so, how do we quantitatively measure this effectiveness? In response, we first propose an empirical protocol based on a fair benchmarking framework to investigate the performance discrepancy between simple methods and GNNs. We further propose a novel metric to quantify the dataset effectiveness by considering both dataset complexity and model performance. To the best of our knowledge, our work is the first to thoroughly study and provide an explicit definition for dataset effectiveness in the graph learning area. Through testing across 16 real-world datasets, we found our metric to align with existing studies and intuitive assumptions. Finally, we explore the causes behind the low effectiveness of certain datasets by investigating the correlation between intrinsic graph properties and class labels, and we developed a novel technique supporting the correlation-controllable synthetic dataset generation. Our findings shed light on the current understanding of benchmark datasets, and our new platform could fuel the future evolution of graph classification benchmarks.
Graph Neural Networks (GNNs) have emerged as a prominent framework for graph mining, leading to significant advances across various domains. Stemmed from the node-wise representations of GNNs, existing explanation studies have embraced the subgraph-specific viewpoint that attributes the decision results to the salient features and local structures of nodes. However, graph-level tasks necessitate long-range dependencies and global interactions for advanced GNNs, deviating significantly from subgraph-specific explanations. To bridge this gap, this paper proposes a novel intrinsically interpretable scheme for graph classification, termed as Global Interactive Pattern (GIP) learning, which introduces learnable global interactive patterns to explicitly interpret decisions. GIP first tackles the complexity of interpretation by clustering numerous nodes using a constrained graph clustering module. Then, it matches the coarsened global interactive instance with a batch of self-interpretable graph prototypes, thereby facilitating a transparent graph-level reasoning process. Extensive experiments conducted on both synthetic and real-world benchmarks demonstrate that the proposed GIP yields significantly superior interpretability and competitive performance to~the state-of-the-art counterparts. Our code will be made publicly available.
Recent works have introduced GNN-to-MLP knowledge distillation (KD) frameworks to combine both GNN's superior performance and MLP's fast inference speed. However, existing KD frameworks are primarily designed for node classification within single graphs, leaving their applicability to graph classification largely unexplored. Two main challenges arise when extending KD for node classification to graph classification: (1) The inherent sparsity of learning signals due to soft labels being generated at the graph level; (2) The limited expressiveness of student MLPs, especially in datasets with limited input feature spaces. To overcome these challenges, we introduce MuGSI, a novel KD framework that employs Multi-granularity Structural Information for graph classification. Specifically, we propose multi-granularity distillation loss in MuGSI to tackle the first challenge. This loss function is composed of three distinct components: graph-level distillation, subgraph-level distillation, and node-level distillation. Each component targets a specific granularity of the graph structure, ensuring a comprehensive transfer of structural knowledge from the teacher model to the student model. To tackle the second challenge, MuGSI proposes to incorporate a node feature augmentation component, thereby enhancing the expressiveness of the student MLPs and making them more capable learners. We perform extensive experiments across a variety of datasets and different teacher/student model architectures. The experiment results demonstrate the effectiveness, efficiency, and robustness of MuGSI. Codes are publicly available at: \textbf{\url{https://github.com/tianyao-aka/MuGSI}.}
In recent years, Graph Neural Networks (GNNs) have become the de facto tool for learning node and graph representations. Most GNNs typically consist of a sequence of neighborhood aggregation (a.k.a., message-passing) layers, within which the representation of each node is updated based on those of its neighbors. The most expressive message-passing GNNs can be obtained through the use of the sum aggregator and of MLPs for feature transformation, thanks to their universal approximation capabilities. However, the limitations of MLPs recently motivated the introduction of another family of universal approximators, called Kolmogorov-Arnold Networks (KANs) which rely on a different representation theorem. In this work, we compare the performance of KANs against that of MLPs on graph learning tasks. We evaluate two different implementations of KANs using two distinct base families of functions, namely B-splines and radial basis functions. We perform extensive experiments on node classification, graph classification and graph regression datasets. Our results indicate that KANs are on-par with or better than MLPs on all studied tasks, making them viable alternatives, at the cost of some computational complexity. Code is available at https: //github.com/RomanBresson/KAGNN.
Graph contrastive learning (GCL) has recently emerged as a new concept which allows for capitalizing on the strengths of graph neural networks (GNNs) to learn rich representations in a wide variety of applications which involve abundant unlabeled information. However, existing GCL approaches largely tend to overlook the important latent information on higher-order graph substructures. We address this limitation by introducing the concepts of topological invariance and extended persistence on graphs to GCL. In particular, we propose a new contrastive mode which targets topological representations of the two augmented views from the same graph, yielded by extracting latent shape properties of the graph at multiple resolutions. Along with the extended topological layer, we introduce a new extended persistence summary, namely, extended persistence landscapes (EPL) and derive its theoretical stability guarantees. Our extensive numerical results on biological, chemical, and social interaction graphs show that the new Topological Graph Contrastive Learning (TopoGCL) model delivers significant performance gains in unsupervised graph classification for 11 out of 12 considered datasets and also exhibits robustness under noisy scenarios.
We present a new class of fast polylog-linear algorithms based on the theory of structured matrices (in particular low displacement rank) for integrating tensor fields defined on weighted trees. Several applications of the resulting fast tree-field integrators (FTFIs) are presented, including (a) approximation of graph metrics with tree metrics, (b) graph classification, (c) modeling on meshes, and finally (d) Topological Transformers (TTs) (Choromanski et al., 2022) for images. For Topological Transformers, we propose new relative position encoding (RPE) masking mechanisms with as few as three extra learnable parameters per Transformer layer, leading to 1.0-1.5%+ accuracy gains. Importantly, most of FTFIs are exact methods, thus numerically equivalent to their brute-force counterparts. When applied to graphs with thousands of nodes, those exact algorithms provide 5.7-13x speedups. We also provide an extensive theoretical analysis of our methods.
Message-Passing Neural Networks (MPNNs) are extensively employed in graph learning tasks but suffer from limitations such as the restricted scope of information exchange, by being confined to neighboring nodes during each round of message passing. Various strategies have been proposed to address these limitations, including incorporating virtual nodes to facilitate global information exchange. In this study, we introduce the Hierarchical Support Graph (HSG), an extension of the virtual node concept created through recursive coarsening of the original graph. This approach provides a flexible framework for enhancing information flow in graphs, independent of the specific MPNN layers utilized. We present a theoretical analysis of HSGs, investigate their empirical performance, and demonstrate that HSGs can surpass other methods augmented with virtual nodes, achieving state-of-the-art results across multiple datasets.